Computation of atomically detailed dynamics of biomolecules, or their reaction pathways, significantly enhances our understanding of their function and enables a better design of new biological materials. Nevertheless, a significant drawback of Molecular Dynamics (MD) simulations is of time scales. At present, routine simulations are not longer than hundreds of nanoseconds of real time. This time is far too short to investigate many biochemical processes, such as conformational transitions, protein activation, or protein folding, which may last from microseconds to minutes. It is proposed to further develop a new methodology (SDEL - Stochastic Difference Equation in Length) to compute bio-molecular dynamics on extended time scales. The new methodology is based on the optimization of an action and a solution of a boundary value problem. It enables the computations of approximate trajectories, in which high frequency modes are filtered out, based on length parameterization of the classical trajectory. The methodology was applied recently to study the folding of the protein Cytochrome C (a millisecond process). Comparison to experimental data was encouraging, and additional insight on the role of non-native contacts during folding has been obtained. It is proposed to extend these studies to include explicit solvent models, and to examine allosteric effects in a protein. It is also proposed to further develop a theory and a computational model that make it possible to extract rate constants from these approximate trajectories.